Stress Evolution Analysis of EM-Induced Void Growth for Multi-Segment Interconnect Wires

Electromigration-induced reliability (EM) is the major concern for design of modern power grids, characterized by high current densities and long metal lines. Due to their high inaccuracy of handling structures with large scale and complexity, traditional empirical EM prediction methods are not applicable for modern power grids. In this paper, we propose a novel analytical model of hydrostatic stress evolution during the void growth phase for general multi-segment wires, common interconnect structures in power grids, based on the adoption of Laplace transformation on Korhonen's equation with coupled boundary conditions (BCs). The analytical solution is expressed with a set of auxiliary basis functions using the complementary error function. With analysis of the analytical expression form, the compact model is presented for practical EM analysis. Compared with the finite element analysis (FEA) results, our compact model can lead to less than 0.50% error on average for multi-segment wires extracted from IBM power grid benchmarks.